That’s the not-so subtle message from various groups, including the American Medical Association, about the dangers of letting anybody older than 70 on the road.

They cause more accidents. They fall asleep. Their reactions are slow. They’re probably losing their minds, let alone their sight. (The AMA calls the safety of older drivers “a public health issue.”)

I recall the story several years ago about an 85-year-old international swimming champion who was stopped by a Peninsula police officer when she was on her way to swimming practice at 6 a.m.

Apparently unclear why somebody of that age would be out in the dark, the young officer asked if something was wrong. When the driver became flustered, she was cited and required to appear in court.

The citation was dismissed, but the woman never forgot her humiliation. She said she had been busted for “driving while old.”

But a study released in June gives older drivers new respect. Ivan Cheung and Anne McCartt, researchers with the Insurance Institute for Highway Safety, a private nonprofit based in Arlington, Va., found that the rate of fatal crashes per licensed driver 70 and older declined by about 37 percent from 1997 to 2008, with the greatest rate decline in drivers age 80 and older.

Even the researchers were surprised. In their study, “Recent Trends in Older Driver Crashes,” they use the words “contrary to expectations” to present their findings.

Analyzing national reports on fatalities and accident reports from 13 states — including California, Florida, Michigan and Ohio — the researchers compared accident rates of drivers involved in fatal and nonfatal crashes between drivers in the 70-74, 75-79 and 80-and-above age ranges with those of drivers ages 35 to 54, the period between perceived adolescent risk-taking and predicted age-related decline.

Among their findings: Fatal crash-involvement rates declined for older and middle-age drivers during this period, but the decline for drivers 70 and older far exceeded the decline for drivers ages 35 to 54. Injury-crash rates declined 34 percent among drivers 80 and older from 1997 to 2005, compared with a 16 percent decrease among 35- to 54-year-olds.

Surprised at their results, researchers speculated as to the reasons. Yes, general highway safety has increased over the years due to several factors, such as increased seat-belt use and improved car design. But something else is happening.

Among possible causes, researchers pointed to restrictive licensing for older drivers in some states, which require regular sight exams and other requirements, “self-policing” by older drivers who recognize their limitations and stay off the road, overall better health among older Americans and improved emergency medical services and trauma care.

Another possibility is that this generation of older drivers has learned from its past. If they’re native Californians, they’ve probably been driving since age 16. If they have survived, they know how to drive.

They’ve had a series of cars. They know the roads. They know the rules. They signal when they change lanes. They don’t tailgate. They come to a full halt at stop signs. They don’t feel the need to run red lights or step on the gas at yellow.

It’s an attitude that comes from experience. And the smartest ones will restrict their driving as they observe their eyesight or other powers decline.

Meanwhile, they deserve our respect.

For a copy of the study, e-mail publications@iihs.org, visit www.iihs.org or write to the Insurance Institute for Highway Safety, 1005 N. Glebe Road, Arlington, VA 22201.

For comments and story ideas, contact Joan Aragone at 650-348-4332 or fogbelt2@aol.com.

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